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- W1995264225 abstract "An explicit construction of surfaces with flat normal bundle in the Euclidean space E n (unit hypersphere S n ) in terms of solutions of certain linear system is proposed. In the case of E 3 our formulae can be viewed as a direct Lie sphere analog of the generalized Weierstrass representation of surfaces in conformal geometry or the Lelieuvre representation of surfaces in affine 3-space. Parametrization of Ribaucour congruences of spheres by three solutions of the linear system is obtained. In view of the classical Lie correspondence between Ribaucour congruences of spheres and surfaces with flat normal bundle in the Lie quadric in P 5 , this gives an explicit representation of surfaces with flat normal bundle in the 4-dimensional space form of the Lorentzian signature. Direct projective analog of this construction is the known parametrization of W -congruences by three solutions of the Moutard equation. Under the Plücker embedding W -congruences give rise to surfaces with flat normal bundle in the Plücker quadric. Integrable evolutions of surfaces with flat normal bundle and parallels with the theory of nonlocal Hamiltonian operators of hydrodynamic type are discussed in the conclusion." @default.
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- W1995264225 date "2001-01-01" @default.
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- W1995264225 title "Surfaces with flat normal bundle: an explicit construction" @default.
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- W1995264225 doi "https://doi.org/10.1016/s0926-2245(00)00042-5" @default.
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